An X-ray CT image is obtained by executing image reconstruction on projection data comprising plural view data which are obtained by performing CT scan based on an X-ray tube and an X-ray detector around an examinee. A false image called an artifact may occur in a reconstructed CT image due to various causes. When an artifact occurs on an image, it disturbs doctor's image diagnosis, and thus an artifact reducing technique corresponding to the type of an artifact has bee developed.
Recently, a multi-slice type X-ray CT apparatus (hereinafter referred to as multi-slice CT) in which plural arrays of detection elements of an X-ray detector are arranged in a body axis direction of an examinee has been popular, and the number of element arrays of the detector has increased. The multi-slice CT can image a broader examinee area by one scan as compared with conventional single slice CT, and thus it brings a great merit that the examination time is shortened. The shortening of the examination time is proportional to the number of the detection element arrays for the same scan speed and the same detection element size. Therefore, the detection element arrays multiply in power of 2, and a multi-slice CT equipped with a detector having 64 arrays of detection elements has been recently sold in the market.
The image reconstructing method of the X-ray CT apparatus is roughly classified into an analytic reconstruction method and an algebraic reconstruction method. The analytic reconstruction method of the image reconstructing method contains a Fourier transform method, a filtered back projection method and a convolution integral method, and the algebraic reconstruction method contains a successive approximation reconstruction method represented by MLEM (Maximum Likelihood Expectation Maximization) method or OSEM (Ordered Subset Expectation Maximization) method. When the analytic method which has been practically used at present is applied to a multi-slice CT having a broad cone angle, it has a problem that a cone beam artifact occurs due to incompleteness of a reconstruction algorithm. On the other hand, the algebraic method is known as having higher completeness than the analytic method, however, it has a problem that a very long calculation time is required because recursive calculation is executed. Therefore, the algebraic method has been hitherto used in a nuclear medicine field, however, it has not been popular in an X-ray CT field. However, the problem that the calculation time of the successive approximation reconstruction method is long has been solved by the recent development of the computer technology, and Patent Document 1 discloses that image formation of an X-ray CT apparatus is performed by using the successive approximation reconstruction method to improve the image quality.
Various methods belonging to the analytic method have been considered as the image reconstructing method of the multi-slice CT at present. With respect to a multi-slice CT having a device with a small number of detection element arrays, for example, four arrays of detection elements, a filtered back projection (Filtered Back Projection) method for a conventional single slice CT can be applied. However, with respect to the larger number of detection elements, for example, a multi-slice CT having 64 arrays of detection elements, adoption of an image reconstructing method called a Feldkamp (Feldkamp) method disclosed in non-patent document 1 or an image reconstructing method corresponding to an improved Feldkamp method has been considered.
The Feldkamp method is an approximation image reconstructing method based on the filtered back projection method. In this method, an effect of an incident angle (cone angle) of X-ray flux (cone beam X-ray) emitted from an X-ray tube to an X-ray detector on the detection element arrays at the end portions is considered, and it is said that occurrence of a cone beam artifact inherent to the multi-slice CT is relatively less.